I am trying to figure out how the 'move out' process at the end of a fixed tenancy works and if a notice has to be given, but my online searches keep returning 'how to end fixed term early', which is a completely different case.

I know from the official website that long term fixed tenancy automatically become periodic at the end and periodic tenancy require a 21 day notice. So for example, if a fixed tenancy ends on Apr 20th and tenant says nothing, can they legally just walk out the door on Apr 20th and stop paying rent or do they need to give notice on Mar 31st (Or would 21 days be counted to March 30th)? Because on March 31st the tenancy is still fixed and will not actually ever become periodic.

Also, what is the landlord's course of action. Particularly two questions 1) Does the landlord need to give some sort of notice of their intentions? So if a landlord says nothing, can the tenant assume that the landlord cannot show up on Apr 19th saying tomorrow you have to leave or that you must sign another fixed term lease? (i.e. you cannot continue with the periodic tenancy)
2) I've seen posts that after fixed tenancy ends the rent may be increased. When would the landlord inform of that if that happens? Does the 60 day notice apply to fixed term contracts or does the transition to periodic term allow to bypass it?

To put this in context: ideally we would like to move to a more suitable location for us, but our concern with today's high housing competition is finding a place we'd be happier in than our current apartment. If we can't find anything in time we'd be okay staying past our fixed term date (if we have that option) and continue searching, but definitely don't want another fixed term tenancy. And certainly don't want any legal technicality surprises!

P.S. Talking to the landlord would be the logical first step but based on our previous experience with them, we are concerned if they know we have interest in leaving, they'd rather we just do it at the end of the term (so they control when they have to look for a replacement) and would force us into a situation where we must move out.